#Dayoon Kim, 2024-4-21, HW24
Help:=proc(): print(` AliceToBob(M,Nbob,eBob,Nalice,dAlice,H), BobReadAlice(MS,Nbob,dBob,Nalice,eAlice,H) `):
print(` AliceT `): end:

#HW24-1.
print(` [8] `);

#HW24-2.

#AliceToBob(M,Nbob,eBob,Nalice,dAlice,H):|
AliceToBob:=proc(M,Nbob,eBob,Nalice,dAlice,H) local x,M1,S:
M1:=M&^eBob mod Nbob:
x:=M&^3 mod H:
S:=x&^dAlice mod Nalice:
[M1,S]:
end:

#BobReadAlice(MS,Nbob,dBob,Nalice,eAlice,H)
#inputs a signed message MS=[M1,S] sent from Alice,
#Nbob,dBob,Nalice, eAlice, and H outputs
#the deciphered message from Alice and also checks
#that it came from Alice and not from a bad guy
#pretending to be Alice
BobReadAlice:=proc(MS,Nbob,dBob,Nalice,eAlice,H) local M1,S,M,X,X1:
M1:=MS[1]:
S:=MS[2]:
M:=M1&^dBob mod Nbob:
X:=M&^3 mod H:
X1:=S&^eAlice mod Nalice:
if X<>X1 then
 print(`You are not Alice, I will call the police`):
fi:
M:
end:

#HW24-3.
#1. my key: 
#MakeRSAkey(10,100);
#[N,e,d]:=[1883925284252198456411, 489703529340811966481, 789424458785472270041]
#H:=94380271871

#2. JOSEPH K sent RSA public key:
#N := 1566257182390879657957:
#e := 962437938162041021459:

# Also, NURAY K sent RSA public key:
#N:= 468904957950013467496814665250009902732699
#e:= 338284290575781482185519661165079134629261

#3. I sent to JOSEPH K 
#MS := [1123155140306324520425, 183765706050434746205]
#What's my birthday, and do you believe it's me?

#Also, I sent NURAY
#MS := [174942331535290281251671604437579603069411, 183765706050434746205]
#What's my birthday, and do you believe it's me?

#4. JOSEPH K sent me
#Thanks for sending! I think that your birthday is 7/02/1996 and I believe it's you.

#Also, NURAY sent me 
#07/02/1996 is your birthday, and you are in fact Dayoon!